On the Melnikov functions and limit cycles near a double homoclinic loop with a nilpotent saddle of order \(\hat{m} \)

DOI10.1016/j.jde.2021.04.032zbMath1471.37055OpenAlexW3162840096MaRDI QIDQ2034013

Junmin Yang, Pei Yu, Mao'an Han

Publication date: 18 June 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2021.04.032

zbMATH Keywords

Liénard systembifurcationlimit cycleMelnikov function

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (3)

On the number of limit cycles near a homoclinic loop with a nilpotent cusp of order \(m\) ⋮ Heteroclinic bifurcation of limit cycles in perturbed cubic Hamiltonian systems by higher-order analysis ⋮ Limit cycles near a homoclinic loop connecting a tangent saddle in a perturbed quadratic Hamiltonian system

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